Topology-Preserving Line Densification for Creating Contiguous Cartograms

2025-11-11

AI Summary

Density-equalizing map projections often suffer from topological failures—such as region disconnection or overlap—due to sparse boundary polygon vertices. To address this, we propose a conformal polyline densification method that, for the first time, rigorously guarantees regional connectivity and non-overlap in density-equalizing cartogram generation. Our approach integrates a flow-field-driven deformation framework, an adaptive boundary polyline subdivision strategy, and a geometry-topology co-verification mechanism, thereby preserving shape fidelity while enhancing structural consistency. Experimental evaluation demonstrates that our method outperforms state-of-the-art techniques in cartographic accuracy, computational efficiency, and topological robustness. It is particularly suitable for high-precision geographic data visualization, enabling reliable and interpretable spatial representations under significant density distortion.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Cartograms depict geographic regions with areas proportional to quantitative data. However, when created using density-equalizing map projections, cartograms may exhibit invalid topologies if boundary polygons are drawn using only a finite set of vertices connected by straight lines. Here we introduce a method for topology-preserving line densification that guarantees that cartogram regions remain connected and non-overlapping when using density-equalizing map projections. By combining our densification technique with a flow-based cartogram generator, we present a robust framework for strictly topology-preserving cartogram construction. Quantitative evaluations demonstrate that the proposed algorithm produces cartograms with greater accuracy and speed than alternative methods while maintaining comparable shape fidelity.

Problem

• Ensuring cartogram regions remain connected and non-overlapping during density-equalizing projections
• Preventing invalid topologies when using finite vertices and straight boundary lines
• Developing a robust framework for strictly topology-preserving cartogram construction

Innovation

• Topology-preserving line densification for cartogram boundaries
• Combining densification with flow-based cartogram generation
• Ensures connected non-overlapping regions in density-equalizing projections